= Origin dependence of event-position orthogonality
The <Minkowski inner product> of two event-position <four-vectors> is invariant under a common <Lorentz transformation> fixing the origin, but changes under a common <translation>. It is therefore not a criterion for the causal separation of the events. For example $(cT,0)$ and $(0,R)$ are orthogonal while their separation has squared interval $c^2T^2-R^2$, which can have any sign. Causal classification uses their difference, not their individual positions.
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